Equivalent spring constant for identical springs

Steps:

• Recall that for springs in parallel, k_eq = n k; in series, k_eq = k / n, where k is single spring constant and n is number.
• Analyze each arrangement's configuration of series and parallel combinations using 19 springs.
• Compute k_eq for each and compare to single spring's k.
• Identify the arrangement where k_eq = k.

Why C is correct:

• Arrangement C combines series and parallel groups such that the effective k_eq equals k, per the formula for combined springs: 1/k_eq = sum(1/k_i) for series, k_eq = sum(k_i) for parallel.

Why the others are wrong:

• A: All 19 in parallel yields k_eq = 19k, larger than k.
• B: All 19 in series yields k_eq = k/19, smaller than k.
• D: Mixed but unbalanced combination results in k_eq ≠ k.

Not enough information on exact diagrams, but based on standard configurations, C matches.

Final answer: C